Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 7x - 4$ and $ BC = 4x + 14$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {7x - 4} = {4x + 14}$ Solve for $x$ $ 3x = 18$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 7({6}) - 4$ $ BC = 4({6}) + 14$ $ AB = 42 - 4$ $ BC = 24 + 14$ $ AB = 38$ $ BC = 38$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {38} + {38}$ $ AC = 76$